A similarity measure with uncertainty for incompletely known fuzzy sets

This paper is devoted to the problem of measuring similarity between pieces of uncertain (incomplete) information in the framework of I-fuzzy set theory (Atanassov´s intuitionistic fuzzy sets and interval-valued fuzzy sets). We propose a way of determining an interval-valued similarity measure of I-fuzzy sets that preserves information about the operands´ uncertainty by approximating lower and upper bounds of similarity degrees. We discuss some of the desirable properties of this measure and illustrate it with an example application in recommender systems.